Render a Bezier curve in the game engine
Curves are a unique object type, they won't render without depth in the default renderer and even with depth, they won't render in the BGE as these and paths aren't supported.

To render these, you have to convert to a mesh, use AltC > Mesh from Curve/Meta/.... You can always duplicate and move the original to another layer before converting so you have a backup and in most cases, if the converted mesh is simple enough, you can convert it back to a curve via the same menu.